3D FEA of cemented steel, glass and carbon postsin a maxillary incisor

Alessandro Lanzaa, Raffaella Aversab, Sandro Rengob,Davide Apicellaa, Antonio Apicellab,*

aDentistry School, Second University of Naples, Naples, ItalybCRIB, Centro Interdipartimentale di Ricerca sui Biomateriali, University of Naples,Federico II, Via Diocleziano 328, 80124 Naples, Italy

Received 15 July 2003; received in revised form 5 August 2004; accepted 16 September 2004

01do

KEYWORDSEndodonticrestorations;Post;Finite elementanalysis;Multiaxial stress

09-5641/$ - see front matter Q 200i:10.1016/j.dental.2004.09.010

* Corresponding author.E-mail address: antonio.apicella@u

Summary Objectives. A comparative study on the stress distribution in thedentine and cement layer of an endodontically treated maxillary incisor has beencarried out by using Finite Element Analysis (FEA). The role of post and cementrigidity on reliability of endodontic restorations is discussed.

Methods. A 3D FEM model (13,272 elements and 15,152 nodes) of a centralmaxillary incisor is presented. A chewing static force of 10 N was applied at 1258angle with the tooth longitudinal axis at the palatal surface of the crown. Steel,carbon and glass fiber posts have been considered. The differences in occlusal loadtransfer ability when steel, carbon and glass posts, fixed to root canal using lutingcements of different elastic moduli (7.0 and 18.7 GPa) are discussed.

Results and significance. The more stiff systems (steel and carbon posts) have beenevaluated to work against the natural function of the tooth. Maximum Von Misesequivalent stress values ranging from 7.5 (steel) to 5.4 and 3.6 MPa (respectively, forcarbon posts fixed with high and low cement moduli) and to 2.2 MPa (either for glassposts fixed with high and low cement moduli) have been observed under a staticmasticatory load of 10 N. A very stiff post works against the natural function of thetooth creating zones of tension and shear both in the dentine and at the interfaces ofthe luting cement and the post. Stresses in static loading do not reach material(dentine and cement) failure limits, however, they significantly differ leading todifferent abilities of the restored systems to sustain fatigue loading. The influence ofthe cement layer elasticity in redistributing the stresses has been observed to be lessrelevant as the post flexibility is increased.Q 2005 Published by Elsevier Ltd. on behalf of Academy of Dental Materials. All rightsreserved.

5 Published by Elsevier Ltd. on

nina2.it (A. Apicella).

Introduction

A persistent problem in clinical dentistry is relatedto fractures occurring in vital or pulp less teeth [1,2].

Dental Materials (2005) 21, 709–715

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behalf of Academy of Dental Materials. All rights reserved.

A. Lanza et al.710

While vertical fractures in vital teeth have beenobserved to occur only in posterior teeth, fracturesin endodontically treated teeth are observed poster-iorly and anteriorly [3–6]. Even if some of thesefractures could be related to concentration offorcesassociated with restoration with posts [7,8], fatigueloading must be considered as additional cause ofroot fracture [1]. Some studies have indicated thatstatic fracture strength of an endodontically treatedintact anterior tooth is not affected or evendecreases with post placement [9] while failureshave been related to fatigue more than maximalloading [10]. The masticatory loads may fluctuate inphase or out of phase and the overall fatigue life isinevitably dictated by the complex phase relationsbetween the principal stress–strain vectors gener-ated in the restored system. The fatigue failure is amulti stage process involving creation of micro-cracks at the interfaces, growth and coalescence ofmicroscopic flaws into dominant cracks and stablepropagation of the dominantmacrocracks accordingto the combination of open, tear and shear modesoccurring in a multiaxial stress condition. The originof multiaxiality depends on factors such as type ofexternal loading, geometry of structure (the stressstate can be multiaxial even if the external appliedload is uniaxial), residual stresses (which are multi-axial by nature) and not homogeneous materialdistribution.

Posts made in unidirectional reinforced compo-site have the mechanical behavior of a beam [27,28] which rigidity is given by a combination of shape(diameter) and type of reinforcement (glass orcarbon). Even if they have been often described tonot reinforce the tooth [29], its role to maintain thecore reconstitution material by unifying it with theroot is particularly true for posterior teeth wheremasticatory functions are essentially compressive[30]. However, when loaded transversely, as is thecase of an incisor, flexural behavior of the postsystems should be carefully considered [31]. Anincisor tooth behaves mechanically like an elasticbeam during function, or more precisely, like abeam fixed at one end, as is a cantilever when notloaded along its longitudinal axis. In such failurescenario, post and core flexural and torsionalcharacteristics should receive more research inter-est [11–13].

Post restorations are then complex systemswhere the stress distribution within the structureis multiaxial, non-uniform and depending on themagnitude and direction of the applied externalloads [14]. Photoelastic analysis [15] and straingauge tests [16,17] provided evidence of complexdeformation behaviors even in presence of smallapplied loads. Previous investigations [17,18] have

also shown that load transfer from post to rootdentine structure differs according to the differentcements used, confirming the occurrence of stressredistribution through the entire root and its role inlighten specific regions from high stress concen-trations, especially at post–dentin interface. Never-theless, direct experimental measurements of thestress distribution at these locations have not beenfound in literature. However, a theoretical wellknown method for calculating stress distributionwithin complex structures is the finite element (FE)method which allows the investigator to evaluatethe influence of model parameter variation oncethe basic model have been correctly defined.Previous investigators have used two-dimensionalaxisymmetric models to describe post and corerestorations mechanical behavior [19–22]. Suchauthors identified regions of stress concentrationsthat could have higher fracture potential and therelevance of some geometrical parameters in postrestoration design. The validity of such analyses hasbeen experimentally established by comparing theresults of simulations with those of laboratory testsor clinical fracture mode observations either whensimple models and surface strain [23] or internalfailure inducing stress distributions [24] wereanalyzed. For the latter cases, the calculatedstresses relate to fracture probability at criticalstress values identifying the necessity of the correctchoice of the failure criterion. The analysis ofnormal as well shear stresses have, in fact, shownlittle failure predictive potential [19] while moreaccurate predictions have been observed usingmaximum principal stresses or Von Mises criteria[20–22]. Fracture, however, are not alwaysdescribed to occur under limiting static loadingconditions. Different critical restoration regionsand fractures patterns are described to occur infatigue testing on titanium and composite post andamalgam cores [25,26] while static strength testing(maximum load applied before failure) of the samesystems leads to same fracture behavior. Theseauthors reported that specimens loaded for morethan 105 cycles showed a gap formation at the core–tooth interface. For the more rigid amalgam andtitanium systems this was induced by the defor-mation of the core at the vestibular side movingaway from the tooth while, for the composite posts,it was induced by the deformation of the dentinefollowing the post intrusion in the tooth. Thedeformations at the dentine interface, whereloads transfer from the post to the dentin occurs,are then described to play a relevant role in definingthe mechanical reliability under fatigue loadings ofpost restorations using different retention systems.Our work analyses the mechanical behavior of an

3D FEA of cemented steel, glass and carbon posts 711

endodontically treated maxillary incisor restoredby different post and cement materials adaptableto dentistry using a FEM analysis.

The present paper evaluates, using Von Misescriteria [20–22], restorative materials performance(types of post and cements) in a maxillary centralincisor using three-dimensional FEA. For the inves-tigation a 3D FEM model with all its anatomic andmaterial characteristics of components (root,crown, root canal and post) is proposed forcomparative evaluations under an ordinary masti-catory load.

Figure 1 FEM model and loading conditions of a postrestored maxillary incisor.

Materials and methods

A linear static structural analysis has been per-formed to calculate the stress distribution in thetooth root canal and luting cement interfaces undera load of 10 N. In order to compare the mechanicalreliabilities of post restorations using differentretention systems and cementing materials(especially under cycling loadings), the complexstress states and redistribution at the dentineinterface, where loads transfer from the postto the dentin occurs, have been analyzed by properchoice of failure criterion.

The choice of the pertinent stress representationcriterion was based on the evaluation of failurepredictive potential of the analysis performed. VonMises (equivalent stresses) energetic criterion hasbeen then chosen as more representative of amultiaxial stress state. Under fatigue loading, infact, the calculated stresses should relate tofracture probability and, therefore, to the assump-tion that different stress states having the sameeffect are equivalent when determining the systemfailure at critical stress values (failure criterion). Insuch cases, accurate predictions have beenobserved [20–22].

Solid and FE models preparation

The solid model was generated using literature data[32] for the dentine, enamel and internal volumesmorphologies, while the external shape of theincisor was obtained by laser based 3D digitiser(Cyberware) of a plaster cast (Thanaka manufac-turer Japan 1978). The scanned profiles wereassembled in a three-dimensional wire framestructure using a 3D CAD (Autocad 12, Autodesk,Inc.) and exported into a 3D parametric solidmodeler (Pro-Engineering 16.0 Parametric Technol-ogies, USA). The tooth volumes were generatedby fitting of the horizontal and vertical profiles.

The geometries and volumes for the cement layerand post were also generated at this stage.

The FEM model was obtained by importing thesolid model into ANSYS rel. 5.3 FEM software(Ansys, Inc. Houston) using IGES format. Thevolumes were redefined in the new environmentand meshed with eight nodes brick with threedegree of freedom per node, finally resulting in amodel with 13,272 elements and 15,152 nodes(section in Fig. 1). Accuracy of the model hasbeen checked by convergence tests. Particularattention has been devoted in the refinement ofthe mesh resulting from the convergence tests atthe cement layer interfaces. Different materialproperties were coupled with the elements andgeometries according to the volume materialdefined in Fig. 1 (gold crown, dentine root, core,cement and post). The carbon and glass fiber postswere considered made by long fibers (carbon orglass fiber) embedded into a polymeric matrix.These composite materials are considered ortho-tropic, so that they show different mechanicalproperties along the fiber direction (x direction)and along the other two normal directions (y and zdirection). The elastic properties of the isotropicmaterials [36] are reported in Table 1. The carbonand glass posts mechanical characteristics [36–38]are reported in Table 2. Ex, Ey, Ez represent theelastic moduli along the three directions while nxy,nxz, nyz and Gxy, Gxz, Gyz are, respectively, thePoisson’s ratios and the shear moduli in theorthogonal planes (xy, xz and yz).

Due to the comparative aim of the structuralevaluations, the given arbitrary commerciallyavailable post geometry has been used:

–

6% conicity, – tip diameter 1.0 mm, – 10 mm insertion depth (about 2/3 of the root

length).

Table 1 The elastic properties of the isotropic materials [36–38].

Material/component Elastic modulus (GPa) Poisson ratio

Gold crown 70 0.30Dentin 18.6 0.32Core (resin composite Biscore, Bisco USA) 12.0 0.33Zinc-oxide phosphate (Dentspy-De Trey, Germany) 22.0 0.35Adhesive cement resin (low modulus) (C&B, Bisco, USA) 7.0 0.28Adhesive cement resin (high modulus) (Panavia, Kuraray,Japan)

18.6 0.28

Steel post 210 0.30

A. Lanza et al.712

A chewing static force of 10 N was applied at 1258angle with the tooth longitudinal axis at the palatalsurface of the crown as indicated in Fig. 1.

All nodes on the external surface of the root from1/3 to root apex were constrained in all directions.

The following assumption have been made:

–

Tm

P

EEEn

n

n

GGG

complete bonding between post and cement wasconsidered,

–

dentine was assumed elastic isotropic materialaccording to Darendelier [33] and Versluis [34],

–

rigid constrains have been considered at rootlevel.

Results and discussion

Attention was firstly directed to the comparison ofthe model results with existing literature clinicaland in vitro experimental observations. Fig. 2 showsthe differences between the stress redistribution ina tooth restored with a steel post (left hand)cemented with zinc oxide phosphate (22 GPa) andwith a carbon post cemented with a softer than(7.0 GPa) and similar to dentine (18.6 GPa) cements(respectively, middle and right hand in Fig. 2)when a buccal load of 10 N (see Fig. 1) is applied.In all cases, maximum equivalent stress occursat the vestibular side of the cement layer

able 2 The elastic properties of the orthotropicaterials [36–38].

roperty Carbon post Glass post

x (GPa) 118 37

y (GPa) 7.20 9.5

z (GPa) 7.20 9.5

xy 0.27 0.27

xz 0.34 0.34

yz 0.27 0.27

xy 2.80 3.10

xz 2.70 3.50

yz 2.80 3.10

(interface between post and cement), which isconsistent with experimentally validated 2D FEA.Stress distribution at the model midplane along thepost-cement interface in the case of steel, carbonand glass posts (cemented with dentine likecements) are reported in Fig. 3. Distances inFig. 3 are measured, as shown in the upper rightside of the same figure, from the apex of the post toits coronal region (crown) along the longitudinalaxis at the model midplane. In both cases, the stressuniformly increases from apex to its maximumvalue located between 1/2 and 2/3 of the rootinsertion, progressively from carbon to steel posts,and than it decreases. As reported in Fig. 2, theequivalent stress reaches maximum value of7.5 MPa for the steel post and 3.6 and 5.4 MPa forthe carbon posts cemented with softer than anddentine like cements, respectively. However, evenif significantly different load transfer character-istics from post to root occur in the three casesexamined, no differences are evident at level ofexternal root structure either for stress distributionand intensities (stress is uniformly distributed andreaches a value of about 3 MPa). These observationsare qualitatively in agreement with the experimen-tal literature using external strain gauge measure-ments [23–35]. In particular, the investigation on

Figure 2 Von Mises equivalent stress comparisonbetween steel and carbon posts cemented with hard(center) and soft (right) luting cements.

Figure 3 Von Mises equivalent stress distribution alongthe root canal maximum stress area (dotted line) for steel(upper curve), carbon (middle curve) and glass lowercurve) composite posts.

3D FEA of cemented steel, glass and carbon posts 713

central incisor teeth [35] showed differences in loadtransfer capability of cast post when differentcements where used. Although details on elasticproperties of the different luting materials were notreported and, hence comparative local stresseswere not evaluated, it was clearly stated that theuse of a cement resulted in an even distribution ofstress throughout the entire external root surfaceand that no differences in strain gauge measure-ments were found between the different cementa-tion media.

A still more favorable stress distribution has beenobserved in the case of restoration using moreflexible glass post. The stress differences betweenthe steel and glass restored tooth are reported inFig. 4. As discussed before, the stress reaches amaximum value of 7.5 MPa for the steel post whileit reaches a significantly lower value of 2.2 MPa foreither glass posts cemented with softer than anddentine like cements. Therefore, there was not asignificant difference in the stress distribution atdentin interfaces for the glass post restored tooth

Figure 4 Von Mises equivalent stress comparisonbetween steel and glass reinforced posts cemented withhard (center) and soft (right) luting cements.

cemented with materials of different rigidity(Fig. 4). This observation leads to the conclusionthat the more flexible the posts are, the less therigidity of the cementing medium is relevant.Moreover, although the stress generated at thepost-cement interfaces in both restoration design(Figs. 2 and 4) were significantly different forsystems restored with different post and cementtype, neither absolute values reached material(dentine, cement or post) failure limits [36].

Conclusion

The placement of an endodontic post creates anunnatural restored structure since it fills the rootcanal space with a material that has a definedstiffness unlike the pulp. Hence it is not possible torecreate the original stress distribution of thetooth. Steel posts are the most dangerous for theroot, potentially leading to its fracture. Evenworking on the cement layer stress absorbingcapability by using less rigid cements is not possibleimprove the stress arising in the system because ofthe high rigidity of the steel post. In a carbon postreconstruction, the elastic modulus of the cementlayer strongly influences the stress absorbingcapability of the system. The glass reconstructionsystem gives the most benign stressing condition; inthis case the cement layer rigidity is less relevantcompared to the carbon post configuration. Clini-cally both carbon and glass posts are subjected todebonding/loosening phenomena that could easilyoccurs in system restored with more rigid cements,toughened cement systems could improve therestoration reliability by opposing to mechanicalprogression of failure and crack growth. Carbon andglass posts debonding does not cause damage totooth tissues.

Static loading at intensities of the masticatoryforces, then, has been shown to be of the order of 2–8 MPa, which are well below the system criticalfailure stress levels. Masticatory function cyclingload, however, could more easily favor crack growthand propagation in restored teeth characterized byhigher levels of localized stresses at the criticalinterfaces such those between dentine and lutingcement. Spontaneous fatigue root fractures havealso be observed to occur even in non-endodonti-cally treated teeth when subjected to heavyrepetitive masticatory loads. Different failuresbehaviors, in fact, have been experimentallyobserved to occur on differently post restoredteeth [37]. The results of our study confirm theimportance of the rigidity of post and luting cement

A. Lanza et al.714

in the assessment of the reliability of endodonticallypost restored through the ability of the material toredistribute the stresses at the interface betweendentine and post. Moreover, it has also beenobserved that the effect of the cement layer rigiditybecomes irrelevant when the stiffness is lowered.

The ideal root canal post must be sufficientlyelastic to accompany the natural flexural move-ments of the structure of the tooth, something thata very rigid metal post cannot do [38,39]. A postwith biomechanical properties to those of dentincould be advantageous by reducing the risk of rootfractures of teeth. A very stiff post working againstthe natural function of the tooth creates zones oftension and shear both in the dentine and at theinterfaces of the luting cement and the post. Thesetensions, which intensity depends on the differ-ences between the relative rigidities of the externalroot and cemented post, can cause cracks orfractures both in the tooth and core reconstitution[25,26]. For this reason we presume that clinicallyobserved failures were principally due to crackpropagation under occurs fatigue loading: the stressdistribution. Glass and carbon posts exhibit highfatigue and tensile strength, and they have aYoung’s modulus comparable to dentin [37]. More-over, these posts are compatible with Bis-GMA resinused in bonding procedures and so they can bebonded in root canal with adhesive resin cementand bonding systems’ new generation. These bond-ing agents transmit stress between the post and theroot structure, reducing stress concentration andpreventing fracture [37,38]. Bonding between thepost and the cement and between the cement andthe dentin appears an important parameter toachieve optimal behavior of endodontical restor-ations [20].

On the contrary steel post and traditionalcements, being no adhesive and also more rigid thanglass andcarbonposts andadhesive resin cements,donot allow a homogeneous stress distribution.

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